Solutions of Long and Short Questions on Solid States (CHSE and CBSE Class 12th) Solid State 1. Establish a relationship between edge lengths (a), nearest neighbouring distance (d) and radius of atom (r) for body centred cubic unit cell and calculate its packing efficiency. Ans: In BCC unit cell the atom at the centre of the body touches all the atoms at nearest neighbouring corners. In Δ ABC, AC = √( AB 2 + BC 2 ) = √( a 2 + a 2 ) = 2 a 2 = √ 2 a Now in Δ ACD, AD = √( AC 2 + CD 2 ) = √{ ( √ 2 a) 2 + a 2 } = √3a From the figure, AD = √3a = 4r => a = (4/ √3) r => d = AD/2 = 2r = √3a /2 Packing Efficiency: The percent volume occupied by the atoms out of the total volume of the unit cell is called the packing efficiency. P.E = (Volume occupied by the atoms / Volume of the unit cell) X 100 The number of atoms per BCC unit cell is equal to one. P.E = [{1X(4/3) πr 3 }